Nonconservative Lie series: post-Newtonian binary dynamics at 2.5PN

TL;DR

This paper provides an analytical solution for the 2.5 post-Newtonian binary problem, capturing both secular and oscillatory dynamics without eccentricity restrictions, useful for gravitational wave modeling.

Contribution

It introduces a systematic Lie series method to solve nonconservative binary dynamics at 2.5PN, including secular and oscillatory behaviors, with applications to gravitational wave templates.

Findings

Exact reconstruction of Peters-Mathews relations for orbital elements.

Complete dynamics including oscillations for gravitational wave templates.

Method applicable to arbitrary nonconservative systems.

Abstract

We present a fully analytical solution to the dynamics of the non-spinning 2.5 post-Newtonian binary problem, accounting for both the long-term (secular) and short-term (oscillatory) temporal behavior, with no restriction on eccentricity. The radiative degrees of freedom are handled within the nonconservative Hamiltonian framework introduced in a companion paper. In this work, we apply the Lie series method to construct a resonant Birkhoff normal-form and the corresponding generator of the radiation-reaction dynamics. The secular piece reconstructs exactly the Peters-Mathews relations for semi-major axis and eccentricity. The oscillatory piece completes the dynamics and is well suited for gravitational wave templates. The procedure we present in this paper can be systematically employed to cast arbitrary nonconservative systems into extended Hamiltonian form so that the Lie method can be applied.